Geometrically necessary dislocations and incompatible lattice deformations were directly related and characterized in terms of a gradient of the elastic distortion. This measure of geometrically necessary dislocation density could play a natural role in non-local theories of plasticity. Issues concerning hardening and boundary conditions were addressed within the setting of a simple theory.

Geometrically Necessary Dislocations, Hardening and a Simple Gradient Theory of Crystal Plasticity. A.Acharya, J.L.Bassani, A.Beaudoin: Scripta Materialia, 2003, 48[2], 167-72